Modeling Investment Returns

Objective

Modeling future stock and bond market performance is hazardous work.  My objective in doing so is to give a reasonable estimate of the range of future outcomes to help planning in the present.

Gather Data

I first made a list of the total United States stock market return for each month going back 100 years (specifically: 1,318 data points).  Each value in that list was then adjusted for inflation using historical CPI data.  I then made a similar list for the bond market using yearly treasury bond returns for the past 110 years, also adjusted for inflation.

Making Predictions

To predict the value of a well-diversified stock portfolio next month, I take the current value and add the return from a randomly selected month in the list of historical stock returns.  I repeat that procedure a thousand times and order the results from smallest to largest.  The median value among those results is my best guess at where the stock portion of the portfolio will be next month.

To predict the value a year from now, I run the same simulation a thousand times, but instead of just adding one random month’s return, I pick twelve random months and add the returns multiplicatively.  I’m left with a thousand predictions based on historical data for stock market performance over the coming year.  Arrange these from smallest to largest, and you can again plan for anything from the “worst case” to the median to the “best case” scenario.

The same procedure can be used to make predictions 10 years from now, or over any time frame you choose.

The bond portion of a portfolio is basically the same process. I randomly select a value from the historical bond return data, divided by 12 since the data comprises yearly returns, and apply it to the bond portion of the portfolio for each month I’m modeling.

Combine the stock and bond values for a total portfolio prediction.

Example

Let’s start with $10,000 and save an additional $100 every month, equally split between stocks and bonds with no re-balancing.  If we leave it alone, what is the range of real values for this investment plan in 10 years?

Model 10k Example

The model suggests a median case at the start of 2028 around $31000, with a 10% worst case scenario of $24000 and a 90% best case scenario around $43000.

With a couple clicks you can drag the same analysis out to 50 years, and witness once again the power of compound interest, particularly in the best case scenarios:

Model 10k Example 50 years

Past Performance is No Guarantee

The past 100 years has seen the most prolific increase in productivity in the scope of human history, and with it a matching return on capital investments.  Perhaps the next hundred years will be similar, probably they will not.  If the coming decades are better than our recent history, we’re all likely to enjoy a more comfortable financial outlook.

But if the coming decades lag behind past performance, an optimistic forecast could spell financial ruin.  I think it’s worth protecting against the latter, and not the former.  I assume the future will lag past performance, and subtract a fixed amount from the historical data.

The historical real return of stocks in my data set is 7.57% on average.  To be conservative, I uniformly shift the data down to 6.00%.  If an optimist wanted to shift it up to 10%, or a pessimist wanted to shift it down to 2%, the procedures above would remain the same.  I think a slight shift down is both realistic and defensible, so that’s what I use for my financial plans.

Similarly, the real return of bonds in the data set is 3.27% and can be shifted up or down depending on one’s expectations.  I tend to leave that number alone, since it is based on historic treasury returns which typically lag the wider bond market and so are already more conservative in nature.

Conclusion

The objective of this article is to provide transparency to the model I use for projecting investments into the future.  No model is perfect and this one isn’t either.  However, it is grounded in historical fact and adaptable to many situations.  Knowing the best case and worst case scenarios give you a huge advantage in planning over a simple compound interest formula that predicts a uniform return each year.